England · Pearson EdexcelSyllabus
Statistics syllabus, dot point by dot point
Every dot point in the England Statisticssyllabus, with a focused answer for each one. Click any dot point for a worked explainer, past exam questions, and links to related dot points. Written by Claude Opus 4.8, Anthropic's latest AI.
Probability
Module overview →- How do you find the probability of combined events using diagrams and the probability laws?Two-way tables, sample space diagrams, tree diagrams and Venn diagrams for up to three events; mutually exclusive and exhaustive events; the addition law and the multiplication law for independent events.10 min answer →
- How do you handle conditional probability and tell independent from dependent events?Formal notation for independent and conditional events; the multiplication law for independent events; the conditional probability formula; dependent events such as selection without replacement.10 min answer →
- How do you measure probability, and how does relative frequency estimate it?The probability scale and language of likelihood; calculating theoretical probability; estimating probability from data using relative frequency; experimental probability tending to theoretical as trials increase.9 min answer →
- How do you find expected frequencies, and what are absolute and relative risk?Expected frequency from probability; absolute and relative risk expressed as expected frequencies; comparing experimental data with theoretical predictions to detect bias in the design.9 min answer →
Processing, representing and analysing data
Module overview →- How do cumulative frequency graphs and box plots show the median, quartiles and spread?Cumulative frequency diagrams (discrete and grouped); estimating the median, quartiles and percentiles; box plots; comparing distributions using box plots and the interquartile range.10 min answer →
- How do histograms display continuous data, and why is area the key idea?Histograms for continuous data with equal and unequal class widths; frequency density; using area to represent frequency; estimating frequencies within a class; correct use of class boundaries.9 min answer →
- Which charts and graphs display which data, and how do you compare data sets with them?Bar charts (including multiple and composite), line graphs, frequency polygons, population pyramids and choropleth maps; representing, interpreting and comparing data sets shown graphically.9 min answer →
- Which tables and diagrams suit which data, and how do you read and compare them?Tabulation, tally, two-way tables, pictograms, pie charts, stem and leaf diagrams and Venn diagrams; choosing and justifying an appropriate representation; spotting misleading diagrams.9 min answer →
Scatter diagrams and correlation
Module overview →- What does correlation tell you, and why does it not prove causation?Vocabulary of correlation (positive, negative, zero, causation, association, interpolation, extrapolation); describing correlation by inspection as strong or weak; correlation does not imply causation; spurious correlation.9 min answer →
- How do you fit a line to data and use it to make and interpret predictions?Line of best fit by eye through the double mean point; the regression line y = a + bx; interpreting gradient and intercept; using the line for prediction with awareness of interpolation and extrapolation.9 min answer →
- How do Spearman's rank and the PMCC measure correlation, and how do they differ?Calculating and interpreting Spearman's rank correlation coefficient; interpreting Pearson's product moment correlation coefficient; the distinction between rank correlation and product moment correlation.10 min answer →
Statistical distributions
Module overview →- When does the binomial distribution apply, and how do you use it?Characteristics of a binomial distribution; the notation B(n, p); the conditions for a binomial model; the mean np; calculating binomial probabilities for n up to 10.9 min answer →
- How do control charts with warning and action lines monitor a process?Sample means are less spread than individual values; control charts for sample mean, median or range; warning lines at two standard deviations and action lines at three; the action to take when a value falls outside a limit.9 min answer →
- What are the features of a Normal distribution, and what proportions lie within one, two and three standard deviations?Characteristics of a Normal distribution; the notation N(mu, sigma squared); the symmetrical bell shape with equal mean, median and mode; the 68, 95 and 99.7 per cent proportions; conditions for a Normal model.9 min answer →
Statistical inference
Module overview →- How does the capture-recapture method estimate the size of a population you cannot count directly?The Petersen capture-recapture formula to estimate a population size; the assumptions the method relies on and their appropriateness; the role of sample size in the reliability of the estimate.9 min answer →
- How do you use a sample to estimate features of the whole population?Using summary statistics to estimate population characteristics; estimating the population mean from a sample; predicting population proportions; the effect of sample size on reliability and replication.9 min answer →
Summarising data
Module overview →- How do you calculate and choose the right average for a data set?Mode, median and mean for discrete and grouped data; estimating the mean of grouped data with midpoints; linear interpolation for the median; weighted and geometric mean; effect of changes and transformations on averages.10 min answer →
- How do you measure and compare the spread of a data set?Range, quartiles, interquartile range, percentiles, interpercentile and interdecile range; choosing an appropriate measure of spread; pairing a measure of spread with a measure of central tendency.9 min answer →
- How do you describe the shape of a distribution and decide whether a value is an outlier?Skewness by inspection and by calculation; interpreting positive and negative skew; identifying outliers by inspection and using the quartile and standard deviation rules; commenting on outliers in context.9 min answer →
- How do you measure spread with standard deviation and compare values from different data sets?Standard deviation for a set of values and for grouped data; using the mean and standard deviation to compare data sets; standardising values with the standardised score to compare across distributions.10 min answer →
The collection of data
Module overview →- How do you collect reliable, valid data and design questions that are not biased?Sources of data, reliability and validity, designing questionnaires and data collection sheets, open and closed questions, leading questions, pilots, and cleaning data before processing.9 min answer →
- How do you control variables and remove bias so an experiment is a fair test?Identifying and controlling extraneous variables, control groups and matched pairs, sources of bias, sensitivity of content, and the random response technique for sensitive questions.9 min answer →
- How do you choose a sampling method that represents the population without bias?Population, sampling frame and sample; simple random, systematic, stratified, quota, cluster, judgement and opportunity sampling; selecting random members; calculating strata sizes.10 min answer →
- How does the statistical enquiry cycle turn a question into a sound conclusion?The statistical enquiry cycle: planning a hypothesis, recognising constraints, collecting, processing, interpreting and evaluating, with proactive strategies to manage problems.9 min answer →
- How do you classify data, and why does the type decide what you can do with it?Types of data: raw, quantitative, qualitative, categorical, ordinal, discrete, continuous, ungrouped, grouped, bivariate and multivariate; primary versus secondary; explanatory and response variables; grouping into class intervals.9 min answer →
Time series and index numbers
Module overview →- How do index numbers track change over time, and how are RPI, CPI and GDP used?Simple index numbers; chain base index numbers; weighted index numbers; the retail price index, consumer price index and gross domestic product; calculating and interpreting index numbers in context.9 min answer →
- How do you calculate and interpret rates such as crude birth and death rates over time?Rates of change over time including percentage change, births, deaths, house prices and unemployment; calculating crude rates with a given formula; standardised rates at Higher tier; making predictions from rates.9 min answer →
- How do moving averages reveal the trend in seasonal data and support predictions?Time series graphs; identifying trends by inspection and by calculating moving averages; plotting a trend line; interpreting seasonal and cyclic variation; using trends and seasonal effects to predict.10 min answer →